How do you find the common ratio, r, for the geometric sequence that has a1 =100 and a8 =50?

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How do you find the common ratio, r, for the geometric sequence that has a1 =100 and a8 =50?

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Answer 1 · 2016-02-27T22:04:16

$r = (1/2)^(1/7)~~0.9057$

Explanation:

The key to solving this problem is in recognizing what the terms of a geometric sequence look like. If we write a geometric sequence in its most general form, we have:

$a_1 = a_1$
$a_2 = a_1r$
$a_3 = a_1r^2$
...
$a_n = a_1r^(n-1)$

In this case $a_8 = 50$ . But, using $a_1 = 100$ , we have

$50 = a_8 = a_1r^(8-1) = 100r^7$

$=>r^7 = 50/100 = 1/2$

$:.r = (1/2)^(1/7)~~0.9057$

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How do you find the common ratio, r, for the geometric sequence that has a1 =100 and a8 =50?

1 Answer

Explanation:

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